Recent content by Rahmuss

what - Thanks. And that part I understand just fine. There is only a z-component of the electric field, so when I do a cross product, I get both an r-component and a theta-component. gabbagabbahey - So the way you're describing it, the magnetic field seems to come up at the center of the...

Homework Statement The question actually asks for the equation for the magnetic field for the rotating disc; but all I'm after is the direction of the magnetic field. Homework Equations None were given; but I've been using: \nabla \times \vec{E} = -\frac{\partial \vec{B}}{\partial t}...

Ah... Ok. Great! Thanks 2Tesla. That helps a lot. That makes sense now. Ok, I can see why I wasn't getting it. Thanks again.

Ok, I have from my teacher that A = \frac{1}{3}, and that \left\langle S_{x}\right\rangle = \frac{2\hbar}{9}. I can normalize it and get A = \frac{1}{3}; but I can't get the correct expectation value. Here is what I am doing: \left\langle X | S_{x}X\right\rangle = A^{2}\frac{h}{2}[(1+2i)...

Any thoughts on normalizing this? I tried another way and got \frac{1}{3} and another way and I got \frac{16\hbar - 2\hbar i}{18}. And neither of those seem to work. I thought that 1/3 would work; but when I try to find the expectation value I get \frac{\hbar}{2} \frac{13}{3}.

Oh, ok. Great, that's exactly what I needed. Thanks Count Iblis and nrqed and others.

I'm just not sure how to get from my relation: a = \mp ib to: X^{y}_{+} = \frac{1}{\sqrt{2}}\begin{pmatrix}1 \\ i \end{pmatrix} X^{y}_{-} = \frac{1}{\sqrt{2}}\begin{pmatrix}1 \\ -i \end{pmatrix}

Well, after a few days I'm still a bit confused with this problem. According to wikipedia the eigenspinors of S_{y} are: X^{y}_{+} = \frac{1}{sqrt{2}}\left[ \begin{pmatrix}1 \\ i \end{pmatrix}\right] X^{y}_{-} = \frac{1}{sqrt{2}}\left[ \begin{pmatrix}1 \\ -i \end{pmatrix}\right]...

[SOLVED] Electron Spin State and Values Homework Statement An electron is in the spin state: X = A\begin{pmatrix} 1-2i \\ 2 \end{pmatrix} (a) Determine the constant A by normalizing X (b) If you measured S_{z} on this electron, what values could you get, and what is the probability...

Oh, you're right, it's just S_{x}, not S_{x}^{2}. Thanks. And I'll change the vectors (on my homework); but is the rest correct then?

[SOLVED] Expectation Values of Spin Operators Homework Statement b) Find the expectation values of S_{x}, S_{y}, and S_{z} Homework Equations From part a) X = A \begin{pmatrix}3i \\ 4 \end{pmatrix} Which was found to be: A = \frac{1}{5} S_{x} = \begin{pmatrix}0 & 1 \\ 1 & 0...

Err... hey, you're right. :D This idiot thanks you.

Homework Statement Check that the spin matrices (Equations 4.145 and 4.147) obey the fundamental commutation relations for angular momentum, Equation 4.134.Homework Equations Eq. 4.147a --> S_{x} = \frac{\hbar}{2}\begin{pmatrix}0 & 1 \\ 1 & 0 \end{pmatrix} Eq. 4.147b --> S_{y} =...

Count Iblis - I understand what you mean. And that makes perfect sense too, that's a great way of getting the different spins. So wikipedia shows the S_{y} e-spinors as something different. They show: S_{y}: X^{y}_{+} = \frac{1}{\sqrt{2}} \left[ \begin{array}{cc}1 \\i...

nrqed - Right! Yeah, I didn't mean for my example of finding the eigenvalues as the problem that I was trying to solve. So... \begin{pmatrix}-\lambda -i\frac{\hbar}{2} \\i\frac{\hbar}{2} -\lambda \end{pmatrix} = 0 \lambda^{2} =\frac{\hbar^{2}}{4} ---> \lambda = \pm \frac{\hbar}{2}...